Abstract

Time correlation functions yield profound information about the dynamics of a physical system and hence are frequently calculated in computer simulations. For systems whose dynamics span a wide range of time, currently used methods require significant computer time and memory. In this paper, we discuss the multiple-tau correlator method for the efficient calculation of accurate time correlation functions on the fly during computer simulations. The multiple-tau correlator is efficacious in terms of computational requirements and can be tuned to the desired level of accuracy. Further, we derive estimates for the error arising from the use of the multiple-tau correlator and extend it for use in the calculation of mean-square particle displacements and dynamic structure factors. The method described here, in hardware implementation, is routinely used in light scattering experiments but has not yet found widespread use in computer simulations.

Received 08 April 2010Accepted 31 August 2010Published online 15 October 2010

Acknowledgments:

We gratefully acknowledge financial support from EPSRC, through the project (J.R. and B.V.), Grant No.GR/S94711/01 (S.K.S.), Grant No. EP/H016686/1 (B.V.), and an Advanced Research Fellowship (A.E.L.), and B. Loppinet for drawing our attention to the multiple-tau correlators.